Project object on curve face
The way I was able to do it was to use the knife project. All you need to do is make the words 2D with no faces, go into object mode and select the words then shift select the cup and go into edit mode. Then go into the view you are in in the first image and press knife project. The only problem with this is that it will go from the view, so you may have to do each individual letter at a time from different views so you can get it looking as nice as possible. Once you finish projecting it onto the cup you can just select the faces of the words on the cup and extrude them out. Sorry it’s such a time consuming way to do it but I couldn’t figure out anything easier. Please msg me back if you need more details. By the way I was able to successfully 3d print what I made with no errors.